Precise Point Positioning for Mobile Robots using Software GNSS Receiver and QZSS LEX Signal

Transcription

1 23 IEEE/RSJ Iteratioal Coferece o Itelliget Robots ad Systems (IROS) November 3-7, 23. Tokyo, Japa Precise Poit Positioig for Mobile Robots usig Software GNSS Receiver ad QZSS Sigal Taro Suzuki, ad Nobuaki Kubo, Member, IEEE bstract This paper describes outdoor localizatio for a mobile robot usig precise poit positioig (PPP) based o the Quasi-Zeith Satellite System (QZSS) L-bad Experimet () sigal. For autoomous avigatio applicatios, a real-time kiematic (RTK) global positioig system (GPS) techique is widely used to estimate user positio with high-precisio accuracy i real time. However, RTK-GPS requires a referece statio, ad there are data acquisitio costs ivolved i estimatig the positio. Our approach corrects positio error by applyig PPP usig the QZSS message. PPP ca estimate a sigle receiver positio without ay referece statio or baselie, through use of satellite positio fixig ad clocks. We developed a method for extractig the QZSS message i real time usig a software GNSS receiver. We the costructed the PPP framework based o a message cotaiig the satellite ephemeris ad clock errors. Fially, we coducted field experimets to evaluate the accuracy ad precisio of our proposed method. The experimetal results cofirmed that our method made a localizatio precisio of.29 m possible without usig a GNSS referece statio. I. INTRODUCTION Recet developmets i itelliget trasportatio system (ITS) related techologies have actively promoted the icreased applicatio of autoomous mobile systems i outdoor eviromets. Examples of such systems iclude automatic vehicle avigatio systems ad umaed costructio systems with autoomous costructio machiery. Mobile mappig systems [], for example, require the ability to carry out cotiuous ad accurate self-positioig. I these applicatios, high-precisio satellite-based positioig costitutes a fudametal part of the applicatio [2]. Global avigatio satellite systems (GNSSs), such as the U.S.-based Global Positioig System (GPS), have traditioally bee used to estimate the positio of mobile robots i outdoor eviromets. The availability of GNSSs is aticipated to improve as ew positioig satellites are lauched. I applicatios that require high-precisio positioig i real time, a real-time kiematic (RTK) GPS techique is usually used [4]. RTK-GPS is oe of the most precise positioig techologies ad ca be used to obtai cetimeter-level accuracy of the positio i real time by processig the carrier-phase measuremets of GPS sigals. I the Defese dvaced Research Projects gecygrad/urba Challege ivolvig driverless outdoor vehicle races, most Taro Suzuki ad Nobuaki Kubo are with the Tokyo Uiversity of Marie Sciece ad Techology, 2--6, Etchujima, Koto-ku, Tokyo , Japa. (phoe ad fax: ; tsuzuk@kaiyodai.ac.jp). teams use RTK-GPS/iertial avigatio system (INS) avigatio. I 25, the Staford Uiversity Racig Team achieved autoomous ruig for over 2 km [3]. RTK-GPS is very popular; however, it requires GNSS base statios or simultaeous observatios by dual-frequecy GPS receivers, which is icoveiet where cost is a cosideratio. I additio, the maximum distace of the user from the referece statio must be less tha 2 km because of ioospheric error, which is depedet o the locatio [5]. Ulike sigle-referece statio RTK-GPS approaches, where the positioig accuracy decreases as the baselie icreases, etwork RTK (NRTK) approaches ideally provide positioig with errors idepedet of the rover positio withi the etwork [5]. However, NRTK also requires a commuicatio lik ad costs are ivolved to receive the correctio data i may cases. I recet years, precise poit positioig (PPP) has bee aticipated as a alterative to RTK-GPS [6][9]. PPP ca estimate a sigle receiver positio without ay referece statio or baselie through the use of satellite positio fixes ad clocks, which are previously determied. I compariso with commo techiques, the costs ca be reduced. However, PPP requires fixed satellite positios ad clocks, ad the questio is how to get these correctio data. I this paper, we use the L-bad Experimet () sigal broadcasted by the Quasi-Zeith Satellite System (QZSS) to solve this problem. The first QZSS was lauched from Japa i September 2 [2]. QZSS uses a asymmetric figure eight orbit, ad hece, the elevatio agle of QZSS is more tha 75 for approximately 8 h/d i Tokyo, Japa [3]. The message provides GPS satellite clock ad ephemeris errors for correctig the GPS positioig error via the QZSS satellite. This fuctio allows the GPS accuracy to be improved. Ufortuately, the messages caot be received usig curret commercial GNSS receivers. I additio, for real-time applicatios, the message eeds be extractable for computig user positios i real time. I this study, we developed a framework for PPP usig the QZSS message for outdoor mobile robots. We also developed a ovel techique for receivig the QZSS message usig a software GNSS receiver. I GNSS research, software-defied receivers (SDR) are widely recogized ad utilized for their cofiguratio flexibility ad ease of use [][]. We were able to costruct the PPP system based o the QZSS message usig a software receiver ad to cofirm the positio estimatio capability i a actual outdoor eviromet. II. OVERVIEW OF PROPOSED METHOD The proposed method to estimate positio usig the QZSS sigal cosists of () message computatio usig a /3/$3. 23 IEEE 369

2 software GNSS receiver, ad (2) localizatio of mobile robots usig PPP with messages. Fig. shows the system flow with a PPP usig the messages. First, we developed the software GNSS receiver to extract the message. I this study, rather tha trackig the sigal, the message was extracted with the aid of the covetioal LC code phase ad the Doppler sigal obtaied by the LC sigal trackig. Usig this method, each GPS satellite ephemeris error ad clock error could be easily used for PPP i a simple cofiguratio. The precise satellite positio ad clock were calculated by the PPP framework. We computed the locatio of the mobile robot ad other ukow values usig a Kalma filter. QZSS GNSS Frot Ed Message Computatio Software receiver GPS Clock Error Ephemeris Error GPS GNSS Receiver Satellite positio ad clock calculatio PPP usig User positio Kalma Filter Figure. Overview of proposed positioig method. There are two parts: () message computatio usig a SDR, ad (2) PPP with messages. III. DECODING OF MESSGE USING SOFTWRE RECEIVER. QZSS Sigal The sigal, a augmetatio sigal i the MHz bad broadcasted from QZSS, is aticipated to provide fie positioig up to the cetimeter level [7][8]. Fig. 2 shows the structure of the message used for the broadcast of the augmetatio iformatio. The message cosists of a 49-bit header, 695 bits of data, ad 256 bits for error correctio usig Reed-Solomo codig; the total size of oe message is 2 bits. The actual data trasfer volume for the augmetatio iformatio is 695 bps, with a basic structure of oe message trasmissio per secod. The augmetatio iformatio for the whole of Japa eeds to be icorporated ito 695 bps. The sigal is overlaid by the ragig code, which has a period of 4 ms ad a chip rate of,23 MChip/s. Header (49 bits) Preamble (32 bits) 2 bits / s Data Part (695 bits) Message Type ID (8 bits) lert Flag ( bit) PRN (8 bits) Figure 2. message structure. Reed-Solomo Code (256 bits) The message cotais the sigal health, ephemeris error, clock error, ad ioospheric correctio. The correctio items such as satellite ephemeris ad clock errors are updated every 2 s for high-speed correctios, ad a low-speed correctio item such as ioosphere error is updated every 3 mi.. Software GNSS Receiver The sigal utilizes code shift keyig (CSK) [7]. CSK modulatio shifts the phase of the code by the umber of chips idicated i the 8-bit ecoded message symbol. The idea proposed i this paper is to decode the messages without the sigal trackig loop for estimatig the code phase ad Doppler frequecy of the sigal, but with the aid of the covetioal LC sigal simultaeously broadcasted from the QZSS. Fig. 3 illustrates the decodig algorithm based o the LC sigal. This algorithm requires a code phase ad Doppler iformatio computed by the LC sigal trackig result to extract the QZSS message. The algorithm was executed as follows: (i) cquisitio ad trackig of the QZSS LC sigal were performed. I the sigal acquisitio, a circular correlatio based o the fast Fourier trasform (FFT) was used to estimate the rough Doppler frequecy ad rough code phase of the LC sigal. I the trackig process, the accurate Doppler frequecy ad code phase were cotiuously estimated every ms usig the frequecy lock loop (FLL), phase lock loop (PLL), ad delay lock loop (DLL). Durig this time, the code phase, which occurs every 4 ms, was ukow. (ii) Sychroizatio of the avigatio bit overlaid i LC code was performed. If the avigatio bit is sychroized, the ambiguity of the code phase (oshifted phase) ca be resolved. We the estimated the Doppler frequecy usig the LC Doppler frequecy. The code phase ad Doppler frequecy of the sigal were deoted usig the LC sigal as follows: C = C L C + ε () d d LC f f LC = (2) where C LC ad C are the code phases, d LC ad d are the Doppler frequecies i LC ad, ad f LC ad f are ad MHz, respectively. The variable ε is the differetial code bias (DC) betwee QZSS LC ad sigals, ad it ca be calibrated i advace. (iii) The code phase (shifted phase) C was estimated usig FFT based o the circular correlatio techique. The message symbol L ca be calculated usig the oshifted code phase ad estimated code phase usig the followig equatio: L = N + C C (3) where N =,23 was the umber of chips of code. 37

3 (iv) The error of the estimated message symbol was corrected by the Reed-Solomo code. O the basis of the above, the GPS satellite ephemeris error ad clock error ca be extracted from the message usig the software GNSS receiver, without trackig the code. LC Iitial Code Phase Iitial Doppler Frequecy FLL Sigal cquisitio Sigal Trackig PLL DLL Code Phase Doppler Frequecy GNSS Frot Ed Code Phase Estimatio usig FFT Message Computatio Reed-Solomo Error Correctio GPS Clock Error Ephemeris Error Figure 3. Flowchart of message extractio aided by LC trackig usig software GNSS receiver. C. Experimet We coducted iitial tests to evaluate the decodig part of the proposed method, usig the test setup show i Fig. 4. We used a frot ed (NSL Stereo, UK), GNSS atea (Trimble Zephyr Model 2, US), ad a laptop PC to receive ad decode the message. Fig. 5 shows the estimated LC ad code phases. We computed the message symbol by takig the differece betwee the LC code phase ad code phase i Fig. 5. The decodig error rate for the message was evaluated usig the Reed-Solomo error correctio code. Fig. 6 shows the relatioship betwee the QZSS elevatio agle ad the decoded symbol errors. Whe the umber of symbol errors is less tha 6, the error ca be corrected by the Reed-Solomo code. I this test, the correct message was received whe the QZSS elevatio agle was over 3. I geeral GNSS positioig, a 5 elevatio maskig is usually used. For this reaso, the QZSS elevatio agle preseted little problem for the GNSS positioig. From these tests, it was cocluded that it is possible to develop a method to receive the QZSS message usig the software GNSS receiver. I the followig sectio, we describe the real-time kiematic PPP that uses the QZSS messages. Laptop PC Frot Ed (NSL STEREO) GNSS tea Figure 4. Set-up of software GNSS reciver. Normalized Power Normalized Power Sample [sample] x ms 4ms Doppler Code phase 23-N byte code phase LC Sample [sample] x 7 Figure 5. Code phases of LC ad sigals obtaied by the proposed method. Number of Decodig Errors QZSS Elevatio gle Decodig Errors Epoch Number Figure 6. Relatioship betwee QZSS elevatio agle ad message symbol decodig errors. IV. PPP WITH MESSGE The PPP was itroduced by Zumberge et al. as a efficiet ad robust aalysis techique for large GPS receiver etworks [6]. PPP ca estimate a sigle receiver positio without ay referece statio or baselie by fixig satellite positios ad clocks to previously determied values. I additio, all positios are related to a well-defied geodetic datum which is valid globally. The Iteratioal GNSS Service (IGS) provides accurate ad high-quality products, icludig GPS satellite orbits ad clocks, based o the post-missio aalysis of observatios at more tha 3 permaet statios worldwide. Furthermore, PPP ca be used for high-precisio positioig without ay baselie legth limitatio. For these reasos, PPP is aticipated to be a useful ad efficiet meas of localizig mobile robots. For the purpose of the real-time applicatio, there was a questio of how to get the precise satellite ephemeris ad clock to process the PPP. s already metioed, we used the QZSS sigal i this study as the precise ephemeris ad clock source usig the software receiver. y obtaiig the precise satellite ephemeris ad clock from positioig satellites usig the GNSS receiver, the applicatios ca easily determie the high-precisio positio without ay data commuicatio. QZSS is suitable for broadcastig the QZSS Elevatio gle deg 37

4 augmetatio iformatio because QZSS has a high elevatio agle, ad it is visible over log periods i Japa. We developed the PPP techique based o the QZSS messages. I the first step, precise satellite clocks ad ephemeris were used for correctig the GNSS observatios. The GNSS carrier-phase observatio was the modeled by Eq. (4) as follows: φ = r + I + T + c( dt dt ) + N + ε (4) Here φ deotes the carrier phase measuremet; r, the geometric satellite-to-receiver distace; I, the ioospheric delay; T, the tropospheric delay; c, the velocity of light; dt, the clock bias of the receiver; dt, the clock bias of the satellite; N, the carrier-phase iteger ambiguity; ad ε, the measuremet error icludig the multipath effect. I covetioal RTK-GPS, the double-differece techique ca be applied to cacel out most of the correlated errors i observatios. I cotrast, PPP uses the observable ioosphere-free liear combiatio (LC) of the dual-frequecy carrier-phase GPS to estimate the user positio. Usig the ioosphere-free LC, the ioosphere delay ca be completely cacelled. The ioosphere-free LC of the dual-frequecy carrier-phase GPS observables was expressed as follows [4]: f φ f φ φ = c = r + T + c( dt dt ) + + ε (5) 2 2 N 2 2 f f 2 where subscripts ad 2 refer to the L ad L2 frequecies, respectively; φ, the carrier phase of the ioosphere-free LC; Ν, the carrier-phase iteger ambiguity of ioosphere-free LC; ad ε, the measuremet error, icludig the L ad L2 multipath effects. Here, the clock bias dt of the satellite ca be calculated from the broadcasted clock ad clock error iformatio. Oce the low-rate clock errors are obtaied, higher rate values ca be acquired by a simple liear iterpolatio, wherei they are assumed to be stable for a short period. The geometric distace r was iteratively computed as follows, usig the satellite ad receiver positios ad cosiderig Earth s rotatio durig the sigal travel time: T s T ( t r c dt) ( r ( t r c dt) U ( t dt) rr r = U / / (6) where U is the Earth-cetered Iertial (ECI) to Earth-cetered Earth-fixed (ECEF) trasform matrix, r S is the satellite positio i ECEF coordiates, ad r r is the user positio i ECEF coordiates. This satellite positio ca be computed by the ephemeris iformatio cotaied i the message. The iterative method was used to solve this light-time equatio. I Eqs. (5) ad (6), the ukow parameters, the tropospheric delay T, ad the carrier-phase iteger ambiguity of ioosphere-free LC Ν, remai. The tropospheric delay T was also obtaied with the tropospheric zeith total delay (ZTD) ad a appropriate mappig fuctio. Values of ZTD, Ν, ad user positio r r were estimated simultaeously by the exteded Kalma filter (EKF) i this study. The state vector x of EKF for state k is deoted as follows: k T [ r dt ZTD N N ] T x = (7) r Here, r r is the 3-D positio vector, ad deotes the umber of satellites. I the EKF predictio step, the equatio of state at predictio was as follows: [ r T ZTD N N ] T x = dt (8) k k r k k k Where the suffix k k deotes state k predictios estimated from the k state. The variables r r ad dt are the receiver positio ad clock error that are calculated by the sigle-poit positioig. I the kiematic PPP, the receiver positio was reset to the sigle-poit positioig solutio i every epoch. I the EKF observatio step, the GPS observatio vectors are deoted as follows: k [ φ φ ] T z = (9) where φ is the ioosphere-free LC carrier phase i Eq. (5). The observatio matrix H is deoted by the followig equatio: H k r = r / r rk k c ZTD / T () / r rk k c ZTD / T The state x ad the covariace matrix P for state x are updated by the geeral Kalma filter framework usig Eq. (). Usig these equatios, the states were compesated by the EKF, ad the user positio was estimated based o the sigle-receiver observatios with the QZSS message. V. ROOT EXPERIMENT We coducted robot tests to evaluate our proposal for positio estimatio usig the PPP based o the QZSS sigal. We compared the two positioig methods, which were () the ormal poit-positioig result output from the GPS receiver, ad (2) the proposed PPP, which employed augmetatio iformatio of messages obtaied by usig the software GNSS receiver.. Test Settigs The positioig test was performed durig a robot competitio for autoomous avigatio of itelliget robots o a crowded walkway, called the Tsukuba Real World Robot Challege. The Challege was held i Tsukuba, Ibaraki, Japa, o November 5, 2. The travel route was part of the Challege course ad is show i Fig. 7. time series of color fish-eye images that shows the course eviromet is also 372

5 icluded i Fig. 7. This figure shows that the surroudigs of the travel route cosisted of roadside trees i leafy areas ad some buildigs, makig it a eviromet susceptible to satellite maskig. The mobile robot that we used for the test is show i Fig. 8. We istalled the dual-frequecy GNSS receiver, atea, ad software GNSS receiver o the robot. fiber optic gyroscope (FOG) ad wheel ecoder for measurig the attitude ad velocity of the mobile robot were also istalled. To compare the positioig accuracy, we computed the referece RTK-GPS solutio usig the GNSS observatio date at the base statio, which was set up ear the test eviromet. We used dual-frequecy RTK-GNSS fix solutios as referece positios for compariso with the results obtaied by the proposed method. However, a RTK-GNSS fix solutio caot be obtaied whe the umber of satellites is reduced i a actual outdoor eviromet. Therefore, we combied RTK-GNSS fix solutios ad dead reckoig (DR) results based o the Kalma filter usig the FOG ad the wheel ecoder to geerate the referece path. The mobile robot traveled for approximately km at speeds of less tha 4 km/h. The GPS data were obtaied at a rate of Hz ad the elevatio agle mask was set at.. Results The umber of satellites used for positioig is show i Fig. 9; Fig. shows the satellite costellatio at the times ad idicated i Fig. 9. Fig. shows that the QZSS has a high elevatio agle ad therefore we ca receive the sigal from the QZSS eve whe the robot is i a urba area. The period show i Fig. 9 for which GPS sigals could ot be received correspods to the time that the mobile robot was i the idoor area. I additio, there were may istaces where the umber of satellites was decreased because of obstructio by buildigs or trees. We compared the localizatio results to evaluate the two methods, the ormal poit positioig ad the PPP usig messages. The results of the positioig estimatios are show i Fig., icludig the estimated positios ad correspodig to the times ad idicated i Fig. 9. Fig. 2 shows a close-up of positios ad. I both Figs. ad 2, the red lies deote the referece paths computed by the referece dual-frequecy GNSS receiver ad DR, the blue lie idicates the results from the ormal sigle-poit positioig, ad the gree lie idicates the results from our proposed method. These figures show that the ormal poit positioig data was very oisy. I cotrast, the positio estimatio usig our proposed method resulted i ru trajectories early idetical to the referece path, idicatig that the positioig error was successfully corrected. Furthermore, the proposed method estimated a smooth ad cotiuous trajectory. Figure 7. Test eviromet for dyamic evaluatio. (The red solid lie idicates the travel route.) Number of Satellite Epoch Number x 4 Figure 9. Number of satellites used i the test. The umber of satellites is sometimes reduced because of satellite obstructio by buildigs or trees. Figure 8. Robot cofiguratio for localizatio experimet. Figure. GPS ad QZSS satellite costellatio durig the test. 373

6 North [m] North [m] Referece path Referece path PPP usig Sigle Poit Pos Referece path5 Referece path PPP usig Sigle Poit Pos Figure. Compariso of positios estimated by each method. The proposed method, idicated by the gree dots, is more accurate tha the others. North [m] Referece path Sigle Poit Pos. PPP usig Figure 2. Close-up of positio estimated by each method. fter the evaluatios above, we evaluated the error i positio estimated by our proposed method versus the referece positio measuremet results with RTK-GNSS/DR avigatio. Fig. 3 shows the time-series positio distace error with sigle-poit positioig ad with our proposed techique, compared to the referece path. Sometimes the error was icreased because of the multipath effects, but our proposed method makes a fairly accurate, ad i may istaces cotiuous, estimatio of positio distace error. Fig. 4 shows histograms of the distace error from sigle-poit positioig ad from our proposed method, compared to the referece path. Regardig the precisio of the positio estimatio, the distace root mea square (DRMS) error versus the referece path was 3.5 m ad the maximum distace error was m for sigle-poit positioig; these errors were.29 m ad 9.22 m by PPP usig messages. These results show that our proposed method effectively estimated the positio with high precisio. Our experimets demostrated the feasibility of high-precisio positio estimatio i outdoor eviromets with a sigle software GNSS receiver usig QZSS messages obtaied by the receiver. 2D Distace Error [m] Number of Data Sigle Poit Pos. PPP usig Epoch Number x 4 Figure 3. Compariso of distace error for the two methods. The proposed method, idicated by the gree dots, is more accurate Sigle poit Pos. PPP usig D Distace Error [m] Figure 4. Compariso of errors i distace with respect to referece locatios for the two methods. VI. CONCLUSIONS I this paper, we proposed a PPP techique usig a QZSS message for outdoor localizatio of mobile robots. PPP ca estimate a sigle receiver positio without ay referece statio, ad is therefore expected to be a meas of localizatio of mobile robots. We developed a algorithm for a software GNSS receiver to receive the QZSS message ad correct the satellite ephemeris ad clock error. We have also proposed a precise poit positioig techique usig the sigle GNSS receiver based o the QZSS message. We cofirmed the usefuless of this techique through a compariso betwee tests ru i outdoor eviromets ad a referece path 374

7 geerated by RTK-GNSS/DR avigatio. We determied positios with a distace root mea square error of.29 m without use of the GNSS referece statio whe we used PPP with the augmetatio iformatio. We also foud that the proposed localizatio techique was useful ad effective for positio estimatio i outdoor eviromets. future challege is to mitigate the multipath effect usig the satellite selectio techique.we expect that the positioig accuracy ca be further improved usig the determiatio of multipath sigals by the software GNSS receiver. Furthermore, we will evaluate the proposed localizatio method i a greater variety of outdoor eviromets. REFERENCES [] Ishikawa K., mao Y., Hashizume T., Takiguchi J. ad Kajiwara J., Mobile Mappig System for Precise Road Lie Localizatio Usig Sigle Camera ad 3D Road Model, Joural of Robotics ad Mechatroics, vol.9, o. 2, pp. 74 8, 27. [2] Kapla, E. ad Hegarty, C., Uderstadig GPS: Priciples ad pplicatios, 2d Editio, rtech House, osto, 25. [3] S. Thru, et al., Staley, the robot that wo the DRP Grad Challege, Joural of Field Robotics, Vol. 23, No. 9, pp , 26. [4] Morales, Y. ad Tsubouchi, T., DGPS, RTK-GPS ad StarFire DGPS Performace Uder Tree Shadig Eviromets, Proc. of the IEEE Iteratioal Coferece o Itegratio Techology, pp , 27. [5] Lachapelle, G., lves, P., Fortes, LP., Cao, ME. ad Towsed,., DGPS RTK positioig usig a referece etwork, Proceedig of the 3th Iteratioal Techical Meetig Satellite Divisio US Istitute of Navigatio (ION), pp. 65 7, 2. [6] Zumberge, J. F., Hefli, M..: Jefferso, D. C. ad Watkis, M. M., Precise poit positioig for the efficiet ad robust aalysis of GPS data from large etworks, Joural of Geophysical Research 2(3), pp , 997. [7] Japa erospace Exploratio gecy, Quazi-Zeith Satellite System Navigatio Service, Iterface Specificatio for QZSS (IS-QZSS) V.4, Techical report, 22. [8] Saito M, Sato Y, Miya M, Shima M, Omura Y, Takiguchi J, sari K, Cetimeter-class augmetatio system utilizig Quasi-Zeith Satellite, Proc. ION GNSS 2, Portlad, Orego, 9-23 September, pp , 2. [9] T. Takasu, Real-time PPP with RTKLI ad IGS real-time satellite orbit ad clock, IGS Workshop 2. [] K. orre, D. M. kos, et al. Software-Defied GPS ad Galileo Receiver: Sigle-Frequecy pproach, Spriger, New York, 27. [] S. Zhao, D. kos, Ope Source GPS/GNSS Vector Trackig Loop -Implemetatio, Filter Tuig, ad Results, i Proceedigs of the 2 Iteratioal Techical Meetig of The Istitute of Navigatio, ION ITM 2, Sa Diego, C, US, Jauary 2, pp [2] M. Kishimoto, E. Myoji, S. Kogure, H. Noda, ad K. Terada, QZSS O Orbit Techical Verificatio Results, I ION GNSS 2, 2. [3]. Hauschild, P. Steigeberger, ad C. RodriguezSolao, Sigal, orbit ad attitude aalysis of Japa s first QZSS satellite Michibiki, GPS Solutios, 6(), pp , 22. [4] Leick,., GPS Satellite Surveyig, 3rd Editio, Joh Wiley & Sos, Ic., Hoboke, New Jersey, US,